To calculate the change in entropy for the complete combustion of 1 mole of methane gas CH4 in oxygen gas O2 at constant pressure and 298 K, we first need to write the balanced chemical equation for the reaction:CH4 g + 2 O2 g CO2 g + 2 H2O g Next, we need the standard molar entropies S for each species involved in the reaction at 298 K. These values can be found in a standard thermodynamic table:S CH4 = 186.3 J/molKS O2 = 205.2 J/molKS CO2 = 213.8 J/molKS H2O = 188.8 J/molKNow we can calculate the change in entropy S for the reaction using the following equation:S = [S products ] - [S reactants ]S = [1 S CO2 + 2 S H2O ] - [1 S CH4 + 2 S O2 ]S = [1 213.8 + 2 188.8] - [1 186.3 + 2 205.2]S = [213.8 + 377.6] - [186.3 + 410.4]S = 591.4 - 596.7S = -5.3 J/molKThe change in entropy for the complete combustion of 1 mole of methane gas CH4 in oxygen gas O2 at constant pressure and 298 K is -5.3 J/molK.